We introduce and study modular Birkhoff–James orthogonality for typical Banach modules B(X, Y) and K(X, Y) , where X and Y are Banach spaces. We present some basic characterizations of modular Birkhoff–James orthogonality under certain restrictions, and completely characterize left symmetric points for the said orthogonality relation in B(X, Y) and K(X, Y). The complications involved in an analogous study of right symmetric points are illustrated through concrete examples.
- (Modular) Birkhoff–James orthogonality
- Bounded linear operator
- Compact operator
- Symmetric point